SPE-167097-MS压裂液及温度对裂缝复杂指数的影响

SPE 167097
Influence of Fracturing Fluid and Reservoir Temperature on Production for Complex Hydraulic Fracture Network in Shale Gas Reservoir
Charles-Edouard Cohen, Xiaowei Weng, Olga Kresse, Schlumberger
Copyright 2013, Society of Petroleum Engineers
This paper was prepared for presentation at the SPE Unconventional Resources Conference and Exhibition-Asia Pacific held in Brisbane, Australia, 11–13 November 2013.
This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright. Abstract
Production from shale reservoirs depends greatly on the efficiency of hydraulic fracturing treatments. Cumulative experience in the industry has led to several best practices in treatment design, which have improved productivity of these reservoirs. Nevertheless, shale reservoirs still bring challenges to stimulation engineers, due to the complex physics involving interactions with natural fractures, stress shadow effects and proppant transport in complex fracture network.
One of the challenges regards fluid and proppant selection, in particular, the issue is how to achieve the desired fracturing fluid viscosity inside the fracture for optimum proppant placement into an expanding complex fracture network. The rheological properties of the fracturing fluid depend on its temperature history, hence understanding the temperature distribution in the hydraulic fracture network is a key consideration for a successful treatment and a more accurate fracture prediction.
This paper investigates the relation between reservoir temperature, fracturing fluid properties and production through fracturing-to-production simulation workflow. The paper first presents a temperature model implemented into the UFM model, which is a comprehensive complex fracturing simulator for shale reservoirs, accounting for interaction with natural fractures, stress shadow effects, and proppant transport in a complex networks. Based on the fracture geometry, proppant placement, and reservoir properties, a semi-analytical production model UPM is used to estimate the production.
This workflow is used to first understand the temperature distribution in the expanding fracture network and understand its evolution as a function of several parameters such as reservoir temperature and rheological properties of the fracturing fluid. Then the associated production forecast provides guidelines on how to achieve optimum proppant and fluid selection based on the reservoir temperature for maximizing production.
Introduction
One particular aspect of shale plays compared to conventional resources regards the critical role that the design and execution of the hydraulic fracturing treatments plays in well productivity. The industry has learnt through many years of trial and error several best practices regarding hydraulic fracturing of shale reservoirs. Often the learning curves begin with the past experiences on conventional reservoirs where the fracture is believed to be bi-wing. Shale reservoirs bring new challenges due to the complex physics involving interactions with natural fractures, stress shadow effects and proppant transport in complex fracture network.
One important parameter to consider is the rheology of the fracturing fluid, which depends on the temperature history inside the fracture network. This will affect both the geometry of the hydraulic fracture network (HFN) and the proppant placement inside the network. Therefore, understanding the temperature distribution in the HFN is important in order to optimize fracture complexity, proppant placement, and ultimately production. The objective of this paper is to investigate the relation between the temperatures inside the HFN, the fluid and proppant selection, and the production, through a simulation workflow.
The simulation workflow uses the UFM model (Weng et al., 2011) for simulating the hydraulic fracturing process. It accounts for interaction with natural fractures, stress shadow effects, and proppant transport in a complex networks. Then the workflow automatically exports the properties of the resulting HFN (geometry, conductivity, ect.) as well as the appropriate reservoir properties to the semi-analytical production model UPM to estimate the production. This workflow was previously described in Cohen et al. (2012) and a previously published parametric study by Cohen et al. (2013) illustrated how it can help understanding some of today’s best practices and be used to optimize treatment design. To simplify the analysis, this
2 SPE 167097 previous work assumed Newtonian rheological behavior for the fracturing fluids and neglected the effect of temperature on the fluid viscosity. In the present paper, the UFM model considers fracturing fluids with power-law fluid behavior and a dependency on temperature and exposure time. Another difference is that the present paper simulates the shut-in until closure of the hydraulic fracture.
This paper starts by describing the temperature model implemented in the UFM model and then presents the base case used in our parametric study. The base case considers a single stage in a single reservoir, but with multiple treatment designs to focus on several fracturing fluids and proppant sizes. Then the simulation workflow is used to analyze the relation between the reservoir temperature and production, as a function of the fracturing fluid type and proppant type.
Temperature model
The modeling of temperature in hydraulic fracturing began in the 60’s. The typical approach is to couple a model for the heat transport in the fracture with a model of the heat exchange with the reservoir at the fracture wall. For the transport part, most models consider only the convection mechanism and neglect the diffusion. This assumption is valid during injection but not during shut-in. Nevertheless, it can also be assumed during shut-in if the focus of the simulation is to predict proppant placement. Modeling of the exchange with the reservoir mostly considers a heat transfer coefficient controlled by the Nusselt number, and the temperature of the fracture face T w. The biggest of the modeling challenges is to find an efficient and accurate way to evaluate T w or similarly the heat flux from the reservoir to the wall. Some approaches are to use analytical or semi analytical expression of the heat transfer into the reservoir, while some others grid inside the reservoir to explicitly calculates its temperature profile.
One of the first temperature models in hydraulic fracturing was proposed by Wheeler (1962), who assumed both conduction and convection inside the fracture but with a constant leak-off velocity. Whitsitt and Dysart (1970), used a Laplace transform but neglected the temperature history of the fracture wall and assumed a linear variation of the leak off rate along the fracture. Several models such as Biot et al. (1987) or Ben-Naceur and Stephenson (1985) used the variational method to approximate the temperature profile inside the reservoir. More recently, Seth et al. (2010) compared a numerical method by gridding the reservoir with an analytical solution using a Green’s function, and also accounted for the diffusion inside the fracture during shut-in.
The model used in this paper is similar to the model used in the fracture simulator by Mack and Elbel (1992) and also the simulator from Adachi et al. (2007). In summary, the model is based on the energy balance equation, and it couples the heat transport equations inside the fracture and the heat exchange with the reservoir, using a superposition method to account for the temperature history, while using a correlation for the leak-off. The exposure time is estimated by using a similar transport equation. Finally, the coupling between the slurry temperature, the exposure time and the rheological properties of the slurry is handled in a separate step. Figure 1 illustrates the domain where the model applies. The main assumptions of the model are:
•Incompressibility of the fluid and the proppant
•Heat source from viscous dissipation is neglected
•No slip boundary condition at the interface between fluid and proppant
•Temperatures of proppant and surrounding fluid are equal
•Heat conduction within the fracturing fluid inside the fracture is neglected
•1D heat transfer from the fracture face to the reservoir.
•The reservoir is a semi-infinite medium with homogenous thermal properties and uniform initial temperature.
The model has been validated against both a commercial fracturing simulator for the case of a bi-wing fracture, and against the analytical solution for the case of a fracture of constant width and height, with a constant injection rate and bottom hole temperature, no leak-off and an infinite heat transfer coefficient. The details of the model and its implementation are discussed in following sections.
SPE 167097 3
Figure 1: Description of the fracture element
Heat transport inside the fracture
Most models in the literature use an equation similar to equation ( 1) inside the fracture, which is the thermal energy balance equation for the slurry, with a source/sink term to account for heat transfer with the reservoir. It can be written either in a non-conservative form like in Kamphuis et al. (1993) as is in this paper, or in a conservative form like in Ribeiro and Sharma (2012) or Ben-Naceur and Stephenson (1985). The conservative form is more comprehensive because it is simply a balance of heat fluxes, while the non-conservative form has the benefit of being simpler to implement because it removes outward fluxes such as leak-off.
This model is valid under the assumptions listed earlier. However, the authors of the present paper did not find in the literature a discussion on the derivation of the equation, thus they propose in Appendix A such derivation. The methodology used is similar to the work presented in Tardy et al. (2012) for modeling temperature during matrix acidizing. The approach taken was to first integrate the total energy equation, kinetic energy and continuity equations on the volume of fluid V f and the volume of proppant V p . Then we apply the volume averaging technique to find average values of the variables. By applying the assumptions and first order approximation we obtain equation ( 1). 〈ߩܥ〉௠
߲〈ܶ〉௠߲ݐ+〈ߩܥܞ〉௠.∇〈ܶ〉௠=1
ܸ௠ඵݍሶ.ܖ݀ݏ஺೑ೝ
( 1) with
〈ߩܥ〉௠=ܿ௙〈ߩܥ〉௙+ܿ௣〈ሺߩܥሻ௣〉௣
( 2) and the following first order approximation 〈ߩܥݒ〉௠≅ܿ௙〈ߩܥ〉௙〈ܞ܎〉௙+ܿ௣〈ߩܥ〉௣〈ܞܘ〉௣ ( 3) In the case of multiple proppant and fluid types we have
ܿ௙〈ߩܥ〉௙=෍
ܿ௙,௞〈ሺߩܥሻ௙,௞〉௙௡೑
௞ୀଵ ( 4) ܿ௣〈ߩܥ〉௣=෍
ܿ௣,௞〈ሺߩܥሻ௣,௞〉௣௡೛
௞ୀଵ
( 5)
Heat transfer between the fluid and the reservoir
The heat transfer between the fluid and the reservoir can be written as the product of the fluid heat conductivity and the temperature gradient inside the fluid at the interface with the reservoir.
ݍሶ=−ߣ௙∇ܶ|௙௥.n fr
( 6) The temperature gradient is not always easy to estimate, particularly in the cases of turbulent flow, significant leak off or complex fluid rheology. This term is typically simplified to the following form
ݍሶ=ℎ௖௢௡௩ሺ〈ܶ〉௠−ܶ௪ሻ
( 7)
Control volume V 0
Volume of fluid V f
Volume of proppant V p Volume of bank V b
A fr
A fp
V f
A fb
n
v fr
4 SPE 167097
The heat transfer coefficient ℎ௖௢௡௩ is defined as a function of the Nusselt number, the thermal conductivity of the fluid phase and the fracture width. The Nusselt number is the ratio between the convective heat transfer with the conductive heat transfer. For most fracturing fluids, a Nusselt number of 4.3 is a good approximation (Meyer (1989)), and is used in this paper. ℎ௖௢௡௩=ܰݑ
ߣ௙ݓ
( 8)
Heat transfer inside the reservoir
The heat transfer inside the reservoir has to account for both the heat conduction through the reservoir and the leak-off. It has been shown (Kamphuis (1990)) that the effect of leak off could be compared to a modification of the thermal conductivity of the reservoir. ම
߲ܶ௥
߲ݐ௏ೝ
݀ݏ=ම∆ሺߢ௘ܶ௥ሻ௏ೝ݀ݏ ( 9) with the effective thermal diffusion coefficient ߢ௘ being
ߢ௘=
ߣ௘
ሺߩܥሻ௥
( 10)
ߣ௘=ߣ௥݁ିఉ
మ
1+݁ݎ݂ሺߚሻ
( 11) ߚ=
ܥ௅
√ߢ
( 12)
The boundary condition is
ඵߢ௘∇ܶ௥.ܖ஺೑ೝ
݀ݏ=−ඵݍሶ஺೑ೝ
݀ݏ=ඵ−ℎ௖௢௡௩ሺ〈ܶ〉௠−ܶ௪ሻ஺೑ೝ
݀ݏ
( 13)
Model implementation
The previous section described how to obtain the appropriate equations to calculate the average temperature in the fracture and in the reservoir. In the present section, we outline the implementation of the solution of these equations.
The UFM model considers two descriptions of the fracture elements, each one for different purposes. For the height growth calculation, and the computation of the fracture properties for the outputs, it uses a rigorous description of the fracture width profile like in Figure 1. For the proppant transport calculation, the UFM model uses a simplified description that considers an average width above the bank and one dimensional fluid flow, as described in Weng et al. (2011) and illustrated in Figure 2.
Figure 2: Simplified description of the fracture element as in the proppant transport model of the UFM model.
z
y
x
w
∆x
H frac
H fluid
SPE 167097 5
Under this description, equation ( 1) can be written as:
〈ߩܥ〉௠
߲〈ܶ〉௠߲ݐ+〈ߩܥݒ〉௠߲〈ܶ〉௠߲ݔ=2
ݓܨ௪ ( 14) With
ܨ௪=ℎ௖௢௡௩ሺ〈ܶ〉௪−〈ܶ〉௠ሻ ( 15)
and 〈ܶ〉௪ being the averaged temperature at the fracture surface. Under a similar assumption of heat transfer in the reservoir
in 1D, in the y direction, the heat transfer equation ( 9) becomes:
߲ܶ௥߲ݐ=ߢ௘߲ܶ௥ଶ
߲ݕଶ ( 16)
With the boundary condition
ߣ௘
߲ܶ௥
߲ݕ
=ℎ௖௢௡௩ሺ〈ܶ〉௪−〈ܶ〉௠ሻ ( 17)
This is valid under the assumption that the conduction inside the reservoir is 1D and that the effective thermal diffusion is homogenous inside the rock. The challenging part is to calculate 〈ܶ〉௪ because the temperatures of both the fluid and the surface of the rock change overtime, and so is the heat transfer coefficient. The approach here is to use the analytical solution for the case of constant flux into a semi-infinite homogeneous medium and then apply the superposition principle to account for the variations in time.
The analytical solution for equation ( 16ሻ and ( 17ሻ is
ܶ௪=ܶ௥௘௦−ܿ଴ܨ଴√ݐ ( 18)
where
ܿ଴=
2ߣ௘ටߢ௘ߨ
( 19)
By applying the superposition principle for piecewise constant heat fluxes, we can write
ܶ௪௡ାଵ=ܶ௥௘௦−ܿ଴෍൫ܨ௪௞ାଵ−ܨ௪௞൯ඥݐ
௡ାଵ−ݐ௞௡
௞ୀଵ
( 20)
Exposure time
The fluid rheology can also depend on the time of exposure to high shear rate and high temperature. To account for this effect, the model keeps track for each fracture element inside the HFN of the time when the fracturing fluid it contains first arrived. Our approach is simply to consider the injection time ߦ௜௡௝like an intrinsic property of the fluid being transported and accumulated inside the HFN. 〈ߩ〉௠߲〈ߦ௜௡௝〉௠
߲ݐ
+〈ߩܞ〉௠.∇〈ߦ௜௡௝〉௠=0 ( 21)
with the boundary condition in the wellbore
ߦ௜௡௝ห
௪௘௟௟௕௢௥௘
=ݐ
( 22) Consequently, the exposure time is defined as ߦ௘௫௣=ݐ−ߦ௜௡௝
( 23)
Base case
The parametric study presented in this paper uses a synthetic case, blending data from a real case from the Marcellus play and data from a case in Cipolla et al. (2009), also representing the Marcellus shale play. The reservoir description is presented in Table 1. The reservoir permeability is 300 nD, the porosity is 3%, the horizontal stress anisotropy is 80 psi, and the initial reservoir temperature (or bottom hole static temperature (BHST)) is 175 F°. The unpropped hydraulic fracture conductivity is 0.001mD.ft.
6
SPE 167097
Table 1: Base case reservoir zone properties
Zone name Top SSTVD (ft) Reservoir pressure (psi)
Min horizontal stress (psi)
Max horizontal stress (psi) Intrinsic permeability
(mD) Porosity (%) Youngs modulus (psi) Poissons ratio 1 5559.86 2787 4905 4965 0.0003 3 3750000 0.23 2 5586.78 2803 4596 4656 0.0003 3 3750000 0.23 3 5653.41 2833 4238 4298 0.0003 3 3750000 0.23 4 5683.41 2833 4207 4267 0.0003 3 3750000 0.23 5 5712.75 2864 4158 4218 0.0003 3 3750000 0.23 6 5752.75 2864 4118 4178 0.0003 3 3750000 0.23 7 5797.75 2864 4142 4202 0.0003 3 3750000 0.23 8 5827.26 2932 4233 4293 0.0003 3 3750000 0.23 9
5867.26
2932
4487
4547 0.0003
3
3750000
0.23
The well considered is a horizontal well, and the base case is a single stage of pumping through four perforation clusters that are 100 ft apart. The pumping schedule is described in Table 2. The study uses fixed proppant concentration and fluid volume but the fracturing fluid can change during all four pumping steps to be of either slickwater, linear gel or cross-linked gel. In addition, it uses four proppant sizes: 80/100, 40/70, 30/50 and 20/40 mesh sands, respectively. Twenty-one combinations of fluid and proppant have been tested in this study, as presented in Table 3.
Table 2: Pumping schedule Step number
Pump rate (bbl/min)
Fluid volume (gal) Fluid
type Proppant type Proppant
concentration (ppa)
1 60 20000 Pad 0
2 60 60000 Fluid 1 proppant 1 0.5
3 60 60000 Fluid 2 proppant 2 1 4
60
60000 Fluid 3 proppant 3
1.5
Treatments one to nine are all using the 40/70 mesh sand first followed by 30/50 mesh sand. The fluid schedule can be a mix of different fluids, with slickwater injected first then followed by either linear gel or cross-linked gel. These treatment designs are aimed at comparing different hybrid job designs. Treatments ten to twenty one are using only one fluid type and one proppant size in each treatment schedule, to investigate the relation between proppant and fluid selection.
Table 3: List of fluid an proppant selections for all treatment design
Treatment number Pad Fluid 1 Fluid 2 Fluid 3 Proppant 1 Proppant 2 Proppant 3
1 L L L L 40/70 40/70 30/50 Multiple fluid and
proppant 2 SW L L L 40/70 40/70 30/50 3 SW SW L L 40/70 40/70 30/50 4 SW SW SW L 40/70 40/70 30/50 5 SW SW SW SW 40/70 40/70 30/50 6 XL XL XL XL 40/70 40/70 30/50 7 SW XL XL XL 40/70 40/70 30/50 8 SW SW XL XL 40/70 40/70 30/50 9 SW SW SW XL 40/70 40/70 30/50 10 SW SW SW SW 80/100 80/100 80/100 Single fluid and proppant
11 SW SW SW SW 40/70 40/70 40/70 12 SW SW SW SW 30/50 30/50 30/50 13 SW SW SW SW 20/40 20/40 20/40 14 L L L L 80/100 80/100 80/100 15 L L L L 40/70 40/70 40/70 16 L L L L 30/50 30/50 30/50 17 L L L L 20/40 20/40 20/40 18 XL XL XL XL 80/100 80/100 80/100 19 XL XL XL XL 40/70 40/70 40/70 20 XL XL XL XL 30/50 30/50 30/50 21 XL XL XL XL 20/40 20/40 20/40
The properties of the proppant are described in Table 4.
Table 4: Proppant sizes
Proppant type Average proppant diameter (in) Specific gravity 80/100 0.006469 2.65 40/70 0.01106 2.65 30/50 0.0169 2.65 20/40 0.02126 2.65
SPE 167097 7
The three fluids have rheological properties described by a power law model, with n’ and k’ being dependant on the temperature and the exposure time. To illustrate their behavior, Figure 3 shows the apparent viscosity at a shear rate of 100s -1 for all three fluids, as a function of temperature and exposure time.
Figure 3: Apparent viscosity at a shear rate of 100s-1, for the three fluids selected (slickwater, linear gel and cross-linked gel)
Figure 3 shows first that the three fluids are much more sensitive to temperature than exposure time. At low temperature, the viscosity of the slickwater is much lower than the viscosity of the linear gel, which is lower than the viscosity of the cross-linked gel. The linear gel loses most of its viscosity above 130 F° and 200 F° for the cross-linked gel.
Figure 4 illustrates for treatment 2 the temperature profile inside the HFN at the end of pumping. It shows that the heating of the fracturing fluid occurs over a short distance from the wellbore. This means that rapid changes of the rheological properties of the fluid occur close to wellbore. A detailed discussion on the temperature profile in biwing fractures can be found in Sinclair (1971). Figure 5 shows the exposure time inside the HFN after the end of pumping. Finally, Figure 6 shows
for the same treatment the calculated production flow rate during 3 years and the corresponding cumulative production.
Figure 4: Temperature profile inside the HFN at the end of
pumping for treatment #2.
Figure 5: Exposure time inside the HFN at the end of
pumping for treatment #2.
Figure 6: Production rate and cumulative production for treatment #2
Slick Water (SW) Linear Gel (L) X-Linked Gel (XL)
Temperature (F°)
Exposure time (s)
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250
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80012001600
2000
5001000
M M s c f
M S c f /d
days
Mscf/d
MMscf
8 SPE 167097
Reservoir temperature
The parametric study presented here was performed by changing the temperature of the reservoir from 100 F° to 300 F°, for all twenty-one treatments defined in Table 3. One important assumption is that the reservoir temperature is accounted for only during the stimulation phase, to highlight the influence of the temperature on the effectiveness of the treatment design. Therefore, the production phase is using the same reservoir fluid density and viscosity relation to pressure, and the same reservoir pressure for all simulations.
Fracturing fluids properties
We first present in Figure 7 and Figure 8 the results from treatment one to nine to focus on the effect of the fluid properties.
Figure 7: Cumulative production after 3 years as a function of ratio of linear gel in the treatment schedule for different
reservoir temperature
Figure 8: Cumulative production after 3 years as a function of ratio of cross-linked gel in the treatment schedule for
different reservoir temperature
Figure 7 shows the cumulative production after 3 years as a function of the volume ratio of linear gel in the treatment design, as defined in Table 3, for different reservoir temperatures. The main trend observed is that in general the production increases as the volume of linear gel increases, for all temperature. In addition, the production tends to be lower when the temperature increases.
Figure 8 shows the cumulative production after 3 years as a function of the ratio of cross-linked gel in the treatment design, as defined in Table 3. It shows that from 100 F° to 150 F° the production decreases as the volume ratio of cross-linked gel increases, while from 175 F° to 300 F° the production increases when the volume ratio of cross-linked gel increases.
To better understand these results, Figure 9 shows the cumulative production after 3 years for treatments number one, five and six in Table 3, as a function of the reservoir temperature Thoses treatments use respectively only slickwater, only linear gel and only cross-linked gel. On the side are the proppant concentrations per surface area inside the network for several points of the plot.
0501001502002503000
20406080100
C u m u l a t i v e p r o d u c t i o n a f t e r 3 y e a r s (M M s c f )
ratio of linear gel in treatment (%)
Slickwater + Linear gel
100 degree F
125 degree F 150 degree F 175 degree F 200 degree F 250 degree F
300 degree F 0501001502002503000
20406080100
C u m u l a t i v e p r o d u c t i o n a f t e r 3 y e a r s (M M s c f )
ratio of cross-linked gel in treatment (%)
Slickwater + Cross-linked gel
100 degree F
125 degree F 150 degree F 175 degree F 200 degree F 250 degree F
300 degree F
SPE 167097 9
Figure 9: Center: cumulative production after 3 years as a function of the reservoir temperature for treatment #1 (only slickwater), #5 (only linear gel) and #6 (only cross-linked gel). Left and right: proppant concentration per surface area (lb/ft2).
It shows first that the linear gel is always better than slickwater for all temperatures, and both fluids tend to have declining production with temperature increasing. This is consistent with the general trend observed in Figure 7. The cross-linked gel has a very low production at low temperature and then a sharp increase at 175 F°, which corresponds to the sharp drop in viscosity seen in Figure 3.
As shown in Cohen et al. (2013), optimum production is achieved through a combination of sufficient propped fracture conductivity with maximized propped length. Figure 9 shows that at low temperature (100 F°) the cross-linked gel is very viscous, which generates a lot of width and conductivity but not enough fracture length, limiting the propped length. On the opposite, slickwater creates a large fracture network but the propped length is then limited by the high settling rate. At low temperature, the viscosity of the linear gel is low enough to create some complexity but at the same time is also high enough to carry the proppant into most part of the network. At high temperature, the three fluids have low enough viscosity to generate enough complexity, thus the challenge is to have enough viscosity to reduce the proppant settling rate. Figure 9 shows that at high temperature the cross-linked gel has the most propped length because it has the highest viscosity while the slickwater has greater difficulty carrying proppant deep into the HFN. This dependency of the production on the propped length is illustrated in Figure 10. It is the same plot as in Figure 9, but with the propped length replacing the cumulative production. The main observation is that the trends in Figure 9 and Figure 10 are the same.
50
100
150
200
250
300
100150200250300
C
u
m
u
l
a
t
i
v
e
p
r
o
d
u
c
t
i
o
n
a
f
t
e
r
3
y
e
a
r
s
(
M
M
s
c
f
)
BHST (degree F)
100% Slickwater
100% Linear gel
100% Cross-linked gel
Lb/ft2
10 SPE 167097
Figure 10: Propped length as a function of the reservoir temperature for treatment #1 (only slickwater), #5 (only linear gel) and #6
(only cross-linked gel)
Figure 11 and Figure 12 show the relation of the optimum production for treatment one to nine to reservoir temperature. Figure 11 shows which ratio of linear gel or cross-linked gel gives the best production for a given temperature. It shows that for all temperature the treatment with linear gel should contain as little slickwater as possible, while for the treatments with cross-linked gel the answer is more temperature sensitive. At low temperature, the treatment should have mostly slickwater while at high temperature (above 175 F°) it should contain mostly cross-linked gel. Figure 12 shows the optimum production for each temperature and the trends are similar to Figure 9. At low temperature, the optimum treatment with linear gel performs better; while at high temperature the optimum treatment with cross-linked gel performs slightly better.
Figure 11: ratio of viscous fluid (linear or cross-linked gel) in treatment design of the optimum production as a function of the reservoir
temperature.
Figure 12: optimum production for hybrid treatment with either linear or cross-linked gel, as
a function of reservoir temperature.
Proppant size
In order to study the relation between proppant and fluid selection as a function of the temperature, treatments ten to twenty-one in Table 3 mix different fluid with different proppant size. The results from these simulations are shown in Figure 13, Figure 14, and Figure 15. Figure 13 shows the cumulative production of the treatments with slickwater as a function of the proppant type, for different reservoir temperatures. Figure 14 and Figure 15 are the same as Figure 13 but for the treatments with linear gel and cross-linked gel, respectively.
02000
4000600080001000012000
14000100
150
200
250
300
P r o p p e d l e n g t h (f t )
BHST (degree F)
100% Slickwater 100% linear gel
100% Cross-linked gel
0102030405060708090100
100
150
200
250
300
r a t i o o f v i s c o u s f l u i d i n t r e a t m e n t f o r o p t i m u m p r o d u c t i o n a f t e r 3 y e a r s (%)
BHST (degree F)
Slickwater + Linear gel Slickwater + Cross-linked gel
050100150200250300100
150
200
250
300
O p t i m u m p r o d u c t i o n a f t e r 3 y e a r s (M M s c f )
BHST (degree F)
Slickwater + Linear gel Slickwater + cross-linked gel。